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Functional polytypic programming  use and implementation
, 1997
"... Abstract Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, pattern match ..."
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Abstract Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, pattern matchers, equality functions, unifiers, rewriting functions, etc. Such functions are called polytypic functions. A polytypic function is a function that is defined by induction on the structure of userdefined datatypes. This thesis introduces polytypic functions, shows how to construct and reason about polytypic functions and describes the implementation of the polytypic programming system PolyP. PolyP extends a functional language (a subset of Haskell) with a construct for writing polytypic functions. The extended language type checks definitions of polytypic functions, and infers the types of all other expressions. Programs in the extended language are translated to Haskell.
Monadic Corecursion  Definition, Fusion Laws, and Applications
 Electronic Notes in Theoretical Computer Science
, 1998
"... This paper investigates corecursive definitions which are at the same time monadic. This corresponds to functions that generate a data structure following a corecursive process, while producing a computational effect modeled by a monad. We introduce a functional, called monadic anamorphism, that cap ..."
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This paper investigates corecursive definitions which are at the same time monadic. This corresponds to functions that generate a data structure following a corecursive process, while producing a computational effect modeled by a monad. We introduce a functional, called monadic anamorphism, that captures definitions of this kind. We also explore another class of monadic recursive functions, corresponding to the composition of a monadic anamorphism followed by (the lifting of) a function defined by structural recursion on the data structure that the monadic anamorphism generates. Such kind of functions are captured by socalled monadic hylomorphism. We present transformation laws for these monadic functionals. Two nontrivial applications are also described.
PolyLib  a library of polytypic functions
 In Workshop on Generic Programming (WGP'98), Marstrand
, 1998
"... This paper describes the polytypic functions in PolyLib, motivates their presence in the library, and gives a rationale for their design. Thus we hope to share our experience with other researchers in the field. We will assume the reader has some familiarity with the field of polytypic programming. ..."
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This paper describes the polytypic functions in PolyLib, motivates their presence in the library, and gives a rationale for their design. Thus we hope to share our experience with other researchers in the field. We will assume the reader has some familiarity with the field of polytypic programming. Of course, a library is an important part of a programming language. Languages like Java, Delphi, Perl and Haskell are popular partly because of their useful and extensive libraries. For a polytypic programming language it is even more important to have a clear and welldesigned library: writing polytypic programs is difficult, and we do not expect many programmers to write polytypic programs. On the other hand, many programmers use polytypic programs such as parser generators, equality functions, etc. This is a first attempt to describe the library of PolyP; we expect that both the form and content of this description will change over time. One of the goals of this paper is to obtain feedback on the library design from other researchers working within the field. At the moment the library only contains the basic
Monads, Shapely Functors and Traversals
, 1999
"... This paper demonstrates the potential for combining the polytypic and monadic programming styles, by introducing a new kind of combinator, called a traversal. The natural setting for dening traversals is the class of shapely data types. This result reinforces the view that shapely data types form a ..."
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This paper demonstrates the potential for combining the polytypic and monadic programming styles, by introducing a new kind of combinator, called a traversal. The natural setting for dening traversals is the class of shapely data types. This result reinforces the view that shapely data types form a natural domain for polytypism: they include most of the data types of interest, while to exceed them would sacrice a very smooth interaction between polytypic and monadic programming. Keywords: functional/monadic/polytypic programming, shape theory. 1 Introduction Monadic programming has proved itself extremely useful as a means of encapsulating state and other computational eects in a functional programming setting (see e.g. [12,14]). Recently, interactions between monads and data structures have been studied as a further way for structuring programs. Initially focusing on lists, the studies have been extended to the class of regular datatypes (see e.g. [4,11,1]), with the aim to embo...
Deriving animations from recursive definitions
 In Draft Proceedings of the 14th International Workshop on the Implementation of Functional Languages (IFL’02
, 2002
"... Abstract. This paper describes a generic method to derive an animation from a recursive definition, with the objective of debugging and understanding this definition by expliciting its control structure. This method is based on a well known algorithm of factorizing a recursive function into the comp ..."
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Abstract. This paper describes a generic method to derive an animation from a recursive definition, with the objective of debugging and understanding this definition by expliciting its control structure. This method is based on a well known algorithm of factorizing a recursive function into the composition of the producer and the consumer of its call tree. We developed a systematic method to transform both the resulting functions in order to draw the tree step by step. The theory of data types as fixed points of functors, generic recursion patterns, and monads, are fundamental to our work and are briefly presented. Using polytypic implementations of monadic recursion patterns and an application to manipulate and generate graph layouts we developed a prototype that, given a recursive function written in a subset of Haskell, returns a function whose execution yields the desired animation. 1
Automatic visualization of recursion trees: a case study on generic programming
 Electronic Notes in Theoretical Computer Science
"... Although the principles behind generic programming are already well understood, this style of programming is not widespread and examples of applications are rarely found in the literature. This paper addresses this shortage by presenting a new method, based on generic programming, to automatically v ..."
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Although the principles behind generic programming are already well understood, this style of programming is not widespread and examples of applications are rarely found in the literature. This paper addresses this shortage by presenting a new method, based on generic programming, to automatically visualize recursion trees of functions written in Haskell. Crucial to our solution is the fact that almost any function definition can be automatically factorized into the composition of a fold after an unfold of some intermediate data structure that models its recursion tree. By combining this technique with an existing tool for graphical debugging, and by extensively using Generic Haskell, we achieve a rather concise and elegant solution to this problem. 1
unknown title
, 2005
"... 1 Motivation Writing a language processor from scratch is a daunting task. The current interest in generative approaches, where (parts of) language processors are generated automatically from formal specifications of the language, comes as no surprise. Early examples are parser generators like Yacc ..."
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1 Motivation Writing a language processor from scratch is a daunting task. The current interest in generative approaches, where (parts of) language processors are generated automatically from formal specifications of the language, comes as no surprise. Early examples are parser generators like Yacc [8], which generate parsers from
Towards Merging Recursion and Comonads
, 2000
"... Comonads are mathematical structures that account naturally for effects that derive from the context in which a program is executed. This paper reports ongoing work on the interaction between recursion and comonads. Two applications are shown that naturally lead to versions of a comonadic fold op ..."
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Comonads are mathematical structures that account naturally for effects that derive from the context in which a program is executed. This paper reports ongoing work on the interaction between recursion and comonads. Two applications are shown that naturally lead to versions of a comonadic fold operator on the product comonad. Both versions capture functions that require extra arguments for their computation and are related with the notion of strong datatype. 1 Introduction One of the main features of recursive operators derivable from datatype definitions is that they impose a structure upon programs which can be exploited for program transformation. Recursive operators structure functional programs according to the data structures they traverse or generate and come equipped with a battery of algebraic laws, also derivable from type definitions, which are used in program calculations [24, 11, 5, 15]. Some of these laws, the socalled fusion laws, are particularly interesting in p...
LPS: A Language Prototyping System Using Modular Monadic Semantics
, 2001
"... This paper describes LPS, a Language Prototyping System that facilitates the modular development of interpreters from semantic building blocks. The system is based on the integration of ideas from Modular Monadic Semantics and Generic Programming. To define a new programming language, the abstract s ..."
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This paper describes LPS, a Language Prototyping System that facilitates the modular development of interpreters from semantic building blocks. The system is based on the integration of ideas from Modular Monadic Semantics and Generic Programming. To define a new programming language, the abstract syntax is described as the fixpoint of nonrecursive pattern functors. For each functor an algebra is defined whose carrier is the computational monad obtained from the application of several monad transformers to a base monad. The interpreter is automatically generated by a catamorphism or, in some special cases, a monadic catamorphism. The system has been implemented as a domainspecific language embedded in Haskell and we have also implemented an interactive framework for language testing. 1
Monads, Shapely Functors and Traversals
"... This paper demonstrates the potential for combining the polytypic and monadic programming styles, by introducing a new kind of combinator, called a traversal. The natural setting for defining traversals is the class of shapely data types. This result reinforces the view that shapely data types form ..."
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This paper demonstrates the potential for combining the polytypic and monadic programming styles, by introducing a new kind of combinator, called a traversal. The natural setting for defining traversals is the class of shapely data types. This result reinforces the view that shapely data types form a natural domain for polytypism: they include most of the data types of interest, while to exceed them would sacrifice a very smooth interaction between polytypic and monadic programming.